reserve T, X, Y for Subset of MC-wff;
reserve p, q, r, s for Element of MC-wff;

theorem Th34:
  (p '&' q) in IPC-Taut iff p in IPC-Taut & q in IPC-Taut
proof
  hereby
A1: (p '&' q) => q in IPC-Taut by Def14;
    assume
A2: p '&' q in IPC-Taut;
    (p '&' q) => p in IPC-Taut by Def14;
    hence p in IPC-Taut & q in IPC-Taut by A2,A1,Def14;
  end;
  assume that
A3: p in IPC-Taut and
A4: q in IPC-Taut;
  p => (q => (p '&' q)) in IPC-Taut by Def14;
  then q => (p '&' q) in IPC-Taut by A3,Def14;
  hence thesis by A4,Def14;
end;
